In a medium mixing bowl, stir together butter, sugar and spices until combined.
Measure 2 tablespoons of butter and roll into a ball. Repeat to make 8 balls. Place on a wax paper-lined baking sheet or plate and chill in the fridge for 1 hour. Transfer to an airtight, food-safe storage container until ready to use.
To make 1 cocktail, boil water. Meanwhile, place 1 ball of spiced butter in a mug and top with the aged rum and blackstrap rum. Add the hot water. Stir until butter melts into the hot rum mixture. Garnish with a cinnamon stick.